Derivata

Derivatans definition:

$f\text{'}\left(x\right)=\underset{h\to 0}{\lim }\frac{f(x+h)-f\left(x\right)}{h}=...$

$\underset{h\to 0}{\lim }\frac{({\left(x+h\right)}^2+(x+h\left)\right)-(x^2+x)}{h}=\underset{h\to 0}{\lim }\frac{x^2+h^2+2hx+h+x-x^2-x}{h}=\underset{h\to 0}{\lim }\frac{h^2+2xh+h}{h}=\underset{h\to 0}{\lim }(h+2x+1)=2x+1$